This paper presents the mathematical framework involved in the determination of an upper bound of the maximum spread value of a D-dimensional Turbo-Code of frame size N. This bound is named Sphere Bound (SB). It is obtained using some simple properties of Euclidian space (sphere packing in a finite volume). The SB obtained for dimension 2 is equal to N. 2. This result has already been conjectured. For dimension 3, we prove that the SB cannot be reached, but can be closely approached (at least up to 95 %). For dimensions 4, 5 and 6, the construction of particular interleavers shows that SB can be approached up to 80%. Moreover, from the SB calculation, an estimate of the minimum Hamming weight of the weight-two input sequence is derived.

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This paper presents a novel analog turbo decoding architecture allowing analog decoders for long frame lengths to be implemented on a single chip. This is made possible by suitably using slicing techniques which allow hardware reuse and re-configurability. The architecture is applied to a DVB-RCS-like code. It shows a reduction of occupied chip area by a factor of ten when compared to a conventional slice design with no significant performance degradation. A single 27mm² 0.25µm BiCMOS decoder can then decode any frame length from 40 up to 1824 bits.I.

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